Chladni states in Ising Spin Lattices

TL;DR

This paper introduces Chladni states, spectral patterns derived from the interaction Laplacian, to analyze and reconstruct metastable spin configurations in various Ising spin systems.

Contribution

It presents a novel spectral method, Topological Mode Decomposition, for understanding frozen spin states across different magnetic models.

Findings

Chladni states effectively organize metastable configurations.

Topological Mode Decomposition enables reconstruction of frozen spin patterns.

Method applies to ferromagnets, antiferromagnets, and spin glasses.

Abstract

Low-temperature spin dynamics can become trapped in long-lived patterns shaped by the geometry of the interaction network. Here we introduce Chladni states: spin configurations obtained by binarizing the eigenmodes of the interaction Laplacian. These graph-spectral patterns organize the metastable configurations reached by Ising systems under non-ergodic relaxation. The resulting Topological Mode Decomposition provides a compact way to monitor and reconstruct frozen spin configurations in ferromagnets, frustrated antiferromagnets, and spin glasses.